Velocity, Speed, Acceleration, and Deceleration Copyright © 2006 jsd 1 Velocity, Speed, Acceleration, and Deceleration The goal for today is to better understand what we mean by terms such as velocity, speed, acceleration, and deceleration. Let’s start with an example, namely the motion of a ball thrown upward and then acted upon by gravity. A major source of confusion in problems of this sort has to do with blurring the distinction between speed and velocity. The speed s is, by definition, the magnitude of the velocity vector: s := |v|. Note the contrast: When we throw the ball upward: – velocity – – speed – The change in velocity is uniformly downward. The velocity is becoming less upward and/or more downward, which is the same thing. The speed is decreasing during the upward trajectory, and increasing during the subsequent downward trajectory. At this point we have a problem, because the rate-of-change of velocity is called acceleration ... but the rate-of-change of speed is also called acceleration! Obviously this creates enormous potential for confusion. We can begin to untangle things as follows: The rate-of-change of velocity is the vector acceleration. The rate-of-change of speed is the scalar acceleration.

The laws of physics are most simply written in terms of velocity, not speed. In a physics context, the unadorned word “acceleration” probably refers to the vector acceleration, but this is not 100% guaranteed. There is no special word for the opposite of the vector acceleration. The opposite of an acceleration in the +X direction is also an acceleration, namely an acceleration in the −X direction. Scalar acceleration means speeding up. The opposite is called deceleration, which means slowing down. Do not confuse the vector acceleration with the scalar acceleration. The scalar acceleration can be considered one component of the vector acceleration, namely the projection in the “forward” direction (although this is undefined if the object is at rest). To repeat: The vector acceleration is defined to be the change in velocity, per unit time. As the name suggests, it is a vector. This term applies no matter how the acceleration is oriented relative to the initial velocity. There are several possible orientations.

The following table shows how to convert vector language to scalar language in each case: – Vector language – 2 Remarks 2.1 A Step Backwards: Scalar Physics No matter what terminology you use, it is almost always a bad idea to formulate physics problems in terms of speed, so you should stick to describing motion in terms of the vectors: position, velocity, and acceleration (namely the vector acceleration). Specifically, in the case of the ball moving under the influence of gravity, it would be unwise and unhelpful (although possible) to formulate the problem in terms of scalar speed and scalar acceleration. Using these ideas, you could say the ball “decelerates” on the way up and “accelerates” on the way down. That’s literally true, but unhelpfully suggests that the physics is different on the way up and on the way down. (For more about the physics of weight and gravity, see reference 1 .) It would be much better to analyze the problem in terms of velocity (not speed) plus vector acceleration. The vector acceleration is the same throughout the flight, i.e. it has a constant magnitude and a constant direction. It is always directed downward.

2.2 A Step Forward: Acceleration in Spacetime For a much more technical discussion of acceleration, including a discussion of how things accelerate when they are already moving at nearly the speed of light, see reference 2 . Velocity Definition in Physics Velocity Definition in Physics Velocity Definition in Physics What Velocity Means and How To Calculate It Velocity is a measure of distance per unit time. It is a vector quantity, with both magnitude and direction. Mina De La O, Getty Images Updated August 02, 2016. Velocity Definition Velocity is defined as a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time.

The most common way to calculate the constant velocity of an object moving in a straight line is with the formula: r = d / t where r is the rate, or speed (sometimes denoted as v, for velocity, as in this kinematics article ) d is the distance moved t is the time it takes to complete the movement Units of Velocity The SI units for velocity are m / s (meters per second). It may be expressed in any units of distance per time. Other units include miles per hour (mph), kilometers per hour (kph), and kilometers per second (km/s). Sample Velocity Problem A physics student drops an egg off an extremely tall building. continue reading below our video 4 Tips for Improving Test Performance What is the egg's velocity after 2.60 seconds? The hardest part about solving for velocity in a physics problem is selecting the right equation. In this case, two equations may be used to solve the problem.

Using the equation: d = vI*t + 0.5*a*t2 where d is distance, vI is initial velocity, t is time, a is acceleration (due to gravity, in this case) d = (0 m/s)*(2.60 s) + 0.5*(-9.8 m/s2)(2.60 s)2 d = -33.1 m (negative sign indicates direction downward) Next, you can plug in this distance value to solve for velocity using the equation: vf = vi + a*t where vf is final velocity, vi is initial velocity, a is acceleration, and t is time. Since the egg was dropped and not thrown, the initial velocity is 0. vf = 0 + (-9.8 m/s2)(2.60 s) vf = -25.5 m/s Although it's common to report velocity as a simple value, remember it's a vector and has direction as well as magnitude. Usually, moving upward is indicated with a positive sign, and down carries a negative sign. Relating Velocity, Speed, and Acceleration Speed, velocity, and acceleration are all related to each other.

Remember: Speed is a scalar quantity that indicates rate of motion distance per time. Its units are length/time. Velocity is a vector quantity that indicates distance per time and direction. Like speed, its units are length/time, but direction is also cited. Acceleration is a vector quantity that indicates the rate of change of velocity. It has dimensions of length/time2. Velocity and Acceleration - Web Formulas Current Location > Physics Formulas > Mechanics > Velocity and Acceleration Velocity and Acceleration Velocity: Velocity of an object is defined as the speed of an object moving in a definite direction. Velocity of an object can be uniform or variable. It can be changed by changing the object’s speed, direction of motion or both. When an object is moving along a straight line at a variable speed, the magnitude of an object with its rate of motion is described in terms of average velocity. SI unit of velocity – meter/second Average velocity – initial velocity + final velocity 2 v = final velocity During uniform motion, velocity remains constant with time and change in velocity for any time interval is zero. During non-uniform motion, velocity varies with time. It has different values at different instants and at different points of the path.

Hence the change in velocity of the object during any time interval is not zero. Acceleration: The rate of change in the velocity of an object per unit time is referred as acceleration and the kind of motion is known as accelerated motion. The acceleration is positive when it is in the direction of velocity and negative when it is opposite to the direction of velocity. What is the Difference between Speed, Velocity and Acceleration? Definitions: Speed or Velocity? Speed is the rate of motion, or the rate of change of position. It is expressed as distance moved (d) per unit of time(t). Speed is a scalar quantity with dimensions distance/time. Speed is measured in the same physical units of measurement as velocity, but does not contain an element of direction. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components. Common speeds of moving objects For human beings, an average walking speed is about 3 mph (~5 km/h, 1.39m/s), The speed of long distance jogging for average persons is about 6 mph (~10 km/h, 2.7 m/s).

Top athletic sprinters can run at 23.03 mph (~36.85 km/h, 10.24 m/s) within a short distance such as a 200 meters dash. Cycling can average 12 mph (~20 km/h, 5.56 m/s) Car can average 65 mph (~104 km/h, 28.9 m/s ) on highway A 747 Airplane has an average speed 565 mi/hr Acceleration Acceleration, (symbol: a) is defined as the rate of change of velocity. It is thus a vector quantity with dimension length/timeï¿½. In SI units, acceleration is measured in meters/secondï¿½. To accelerate an object is to change its velocity, which is accomplished by altering either its speed or direction (like in case of uniform circular motion) in relation to time. Acceleration can have positive and negative values. Any time that the sign (+ or -) of the acceleration is the same as the sign of the velocity, the object will speed up. If the signs are opposite, the object will slow down. Acceleration is a vector quantity.

When either velocity or direction changes, there is acceleration (or deceleration). To accelerate an object requires the application of a force. Graphing Velocity and Acceleration A car accelerates from rest. The following two graphs are created using a java applet (see below). Physics dictionary (Feimer's Physics Page) Physics Dictionary The Letter A: Absolute zero: lowest possible temperature at which gas would have a zero volume. Absorption spectrum: spectrum of electromagnetic radiation absorbed by matter when radiation of all frequencies is passed through it. Acceleration: change in velocity divided by time interval over which it occurred. Accuracy: closeness of a measurement to the standard value of that quantity. Achromatic lens: lens for which all light colors have the same focal length. Action-reaction forces: pair of forces involved in an interaction that are equal in magnitude and opposition in direction. Activity: number of decays per second of a radioactive substance. Adhesion: force of attraction between two unlike materials. Air resistance: force of air on objects moving through it. Alpha decay: process in which a nucleus emits an alpha particle. Alpha particle: positively- charged particles consisting of two protons and two neutrons emitted by radioactive materials. Ammeter: device to measure electrical current.

Amorphous solid: solids that have no long- range order; no crystal structure. Ampere: unit of electric current; one ampere is the flow of one coulomb of charge per second. Amplitude: in any periodic motion, the maximum displacement from equilibrium. Angle of incidence: angle between direction of motion of waves and a line perpendicular to surface the waves are striking. Angle of reflection: angle between direction of motion of waves and a line perpendicular to surface the waves are reflected from. Angle of refraction: angle between direction of motion of waves and a line perpendicular to surface the waves have been refracted from. Angular momentum: quantity of rotational motion. For a rotating object, product of moment of inertia and angular velocity. Annihilation: process in which a particle and its antiparticle are converted into energy. Antenna: device used to receive or transmit electromagnetic waves. Antineutrino: subatomic particle with no charge or mass emitted in beta decay. Antinode: point of maximum displacement of two superimposed waves. Archimedesï¿½ principle: object immersed in a fluid has an upward force equal to the weight of the fluid displaced by the object. Artificial radioactivity: radioactive isotope not found in nature.

atomic mass unit: unit of mass equal to 1/12 the atomic mass of carbon- 12 nucleus. Atomic number: number of protons in the nucleus of the atom. Average acceleration: acceleration measured over a finite time interval Average velocity: velocity measured over a finite time interval. --------------- Back-EMF: potential difference a cross a conductor caused by change in magnetic flux. Band theory: theory explaining electrical conduction in solids. Baryon: subatomic particle composed of three quarks. Interacts with the strong nuclear force. Battery: device that converts chemical to electrical energy consisting of two dissimilar conductors and an electrolyte. Beat : slow oscillation in amplitude of a complex wave Bernoulliï¿½s principle: when a fixed quantity of fluid flows, the pressure is decreased when the flow velocity increases. Beta decay: radioactive decay process in which an electron or positron and neutrino is emitted from a nucleus. Beta particle: high speed electron emitted by a radioactive nucleus in beta decay. Binding energy: negative of the amount of energy needed to separate a nucleus into individual nucleons. Boiling point: temperature at which a substance, under normal atmospheric pressure, changes from a liquid to a vapor state.

Breeder reactor: nuclear reactor that converts nonfissionable nuclei to fissionable nuclei while producing energy. Bubble chamber: instrument containing superheated liquid in which the path of ionizing particles is made visible as trails of tiny bubbles. Buoyant force: upward force on an object immersed in fluid. --------------- Calorimeter: device that isolates objects to measure temperature changes do to heat flow. Candela: unit of luminous intensity. Capacitance: ratio of charge stored per increase in potential difference. Capacitor: electrical device used to store charge and energy in the electrical field. Capillary action: rise of liquid in narrow tube due to surface tension. Carnot efficiency: ideal efficiency of heat engine or refrigerator working between two constant temperatures. Centripetal force: force that causes centripetal acceleration. Chain reaction: nuclear reaction in which neutrons are produced that can cause further reactions. Charged : object that has an unbalance of positive and negative electrical charges. Charging by conduction: process of charging by touching neutral object to a charged object. Charging by induction: process of charging by bringing neutral object near charged object, then removing part of resulting separated charge.

Chromatic aberration: variation in focal length of lens with wavelength of light. Circular motion: motion with constant radius of curvature caused by acceleration being perpendicular to velocity. Clock reading: time between event and a reference time, usually zero. Closed, isolated system: collection of objects such that neither matter nor energy can enter or leave the collection. Closed-pipe resonator: cylindrical tube with one end closed and a sound source at other end. Coefficient of friction: ratio of frictional force and the normal force between two forces. Coefficient of linear expansion: change in length divided by original length and by temperature change. Coefficient of volume expansion: change in volume divided by original volume and by temperature change. Coherent waves: waves in which all are in step; are in phase. Cohesive force: attractive force between similar substances. Complementary color: two colors that, when added , produce white light. Two pigments, that when combined, produce black. Compound machine: machine consisting of two or more simple machines. Compton effect: interaction of photons, usually X rays, with electrons in matter resulting in increased wavelength of X rays and kinetic energy of electrons. Concave lens: lens thinner in center than edges; a diverging lens.

Concave mirror: converging mirror, one with center of curvature on reflecting side of mirror. Conduction band: energies of charge carries in a solid such that the carries are free to move. Conductor: materials through which charged particles move readily; or heat flow readily. Conserved properties: property that is the same before and after an interaction. Consonance: two or more sounds that, when heard together, sound pleasant. Constant acceleration: acceleration that does not change in time. Constant velocity: velocity that does not change in time. Constructive interference: superposition of waves resulting in a combined wave with amplitude larger than the component waves. Convection: heat transfer by means of motion of fluid. Conventional current: motion of positive electrical current. Converging lens: lens that causes light rays to converge; usually a convex lens. Convex lens: lens that is thicker in the center than at edges. Convex mirror: diverging mirror. Center of curvature is on side opposite reflecting side of mirror. Cosine: the ratio of the adjacent side to the hypotenuse. Coulomb: unit of electrical charge. Charge caused by flow of one ampere for one second. Crest of wave: high point of wave motion.

Critical angle: minimum angle of incidence that produces total internal reflection. Crystal lattice: structure of solid consisting of regular arrangment of atoms. --------------- The Letter D: De Broglie wavelength: length of de Broglie wave of particle; Planckï¿½s constant divided by momentum of particle. Decibel: unit of sound level. Dependent variable: variable that responds to change in manipulated variable. Derived units: unit of quantity that consists of combination of fundamental units. Destructive interference: superposition of waves resulting in a combined wave with zero amplitude. Diffraction: bending of waves around object in their path. Diffraction grating: material containing many parallel lines very closely spaced that produces a light spectrum by interference. Diffuse reflection: reflection of light into many directions by rough object. Dimensional analysis: checking a derived equation by making sure dimensions are the same on both sides. Diode: electrical device permitting only one way current flow. Dispersion of light: variation with wavelength of speed of light through matter resulting in separation of light into spectrum. Displacement: change in position. A vector quantity. Dissonance: two or more sounds that, when together, sound unpleasant. Distance: separation between two points. A scalar quantity.

Diverging lens: lens that causes light rays to spread apart or diverge; usually a concave lens. Dopants: small quantities of material added to semiconductor to increase electrical conduction. Doppler shift: change in wavelength due to relative motion of source and detector. Dynamics: study of motion of particles acted on by forces. --------------- Effective current: DC current that would produce the same heating effects. Effective voltage: DC potential difference that would produce the same heating effects. Efficiency: ratio of output work to input work. Effort force: force extended on a machine. Elastic collision: interaction between two objects in which the total energy is the same before and after the interaction. Elasticity: ability of object to original shape after deforming forces are removed. Electrical charge pump: device, often a battery or generator, that increase potential of electrical charge. Electrical circuit: continuous path through which electrical charges can flow. Electrical current: flow of charged particles. Electrical field: property of space around a charged object that causes forces on other charged objects. Electric field lines: lines representing the direction of electric field. Electric field strength: ratio of force exerted by field on a tiny test charge to that change.

Electric generator: device converting mechanical energy into electrical energy. Electric potential: ratio of electric potential energy to charge. Electric potential difference: difference in electric potential between two points. Electric potential energy: energy of a charged body in an electrical field. Electromagnet: device that uses an electric current to produce a concentrated magnetic field. Electromagnetic force: one of fundamental forces due to electric charges, both static and moving. Electromagnetic induction: production of electric field or current due to change in magnetic flux. Electromagnetic radiation: energy carried by electromagnetic waves throughout space. Electromagnetic waves: wave consisting of oscillating electric and magnetic fields that move at speed of light through space. Electromotive force: potential difference produced by electromagnetic induction. Electron: subatomic particle of small mass and negative charge found in every atom. Electron cloud: region of high probability of finding an electron around an atom. Electron diffraction: effects on electrons due to wave-like interference of electrons with matter. Electron gas model: description of current flow through conductors. Electroscope: device to detect electric charges. Electrostatics: study of properties and results of electric charges at rest. Electroweak force: unification of electromagnetic and weak forces.

Elementary charge: magnitude of the charge of an electron. 1.602 *10^ -19 Emission spectrum: spectrum produced by radiation from excited atoms. Energy: non-material property capable of causing changes in matter. Energy levels: amounts of energy an electron in an atom may have. Entropy: measure of disorder in a system; ratio of heat added to temperature. Equilibrant force: force needed to bring an object into transitional equilibrium. Equilibrium: condition in which net force is equal to zero. Condition in which net torque on object is zero. Equivalent resistance: single resistance that could replace several resistors. Evaporation: change from liquid to vapor state. Excited state: energy level of atom higher than ground state. External forces: forces exerted from outside a system. Extrinsic semiconductor: semiconductor in which conduction is primarily the result of added impurities. --------------- Factor-label method: dimensional analysis. Farad: unit of capacitance. One coulomb per volt. Ferromagnetic materials: materials in which large internal magnetic fields are generated by cooperative action of electrons. First harmonic: in music, the fundamental frequency.

First law of thermodynamics: change in internal or thermal energy is equal to heat added and work done on system. Same as law of conservation of energy. Fluid: material that flows, i.e. liquids, gases, and plasmas. Focal length: distance from the focal point to the center of a lens or vertex of a mirror. Focal point: location at which rays parallel to the optical axis of an ideal mirror or lens converge to a point. Forbidden gap: energy values that electrons in a semiconductor or insulator may not have. Force: agent that results in accelerating or deforming an object. Frame of reference: coordinate system used to define motion. Fraunhofer lines: absorption lines in the sunï¿½s spectrum due to gases in the solar atmosphere. Frequency: number of occurrences per unit time. Friction: force opposing relative motion of two objects are in contact. Fundamental particles: those particles( i.e. quarks and leptons) of which all materials are composed. Fundamental tone: lowest frequency sound produced by a musical instrument. Fundamental units: set of units on which a measurement system is based( i.e. meter, second, kilogram, ampere, candela).

Fuse: metal safety device in an electric circuit that melts to stop current flow when current is too large. Fusion: combination of two nuclei into one with release of energy. --------------- Galvanometer: device used to measure very small currents. Gamma decay: process by which a nucleus emits a gamma ray. Gamma particle: high energy photon emitted by a radioactive nucleus. Gas: state of matter that expands to fill container. Geiger-Mueller tube: device used to detect radiation using its ability to ionize matter. General theory of relativity: explanation of gravity and accelerated motion invented by Einstein. Gluon: carrier of strong nuclear force. Grand unified theories: theories being developed that unify the stronger and electroweak forces into one force. Gravitational field: distortion of space due to the presence of mass. Gravitational force: attraction between two objects due to their mass. Gravitational mass: ratio of gravitational force to objectï¿½s acceleration. Gravitational potential energy: change of energy of object when moved in a gravitational field. Graviton: particle that carries the gravitational force. Not yet observed. Ground state: lowest energy level of an electron in an atom.

Grounding: process of connecting a charged object to Earth to remove objectï¿½s unbalanced charge. --------------- Half-life: length of time for half of a sample of radioactive material to decay. Harmonics: frequencies produced by musical instrument that are multiples of fundamental tone. Heat: quantity of energy transferred from one object to another because of a difference in temperature. Heat engine: device that converts thermal energy to mechanical energy. Heat of fusion: quantity of energy needed to change a unit mass of a substance from solid to liquid state at the melting point. Heat of vaporization: quantity of energy needed to change a unit mass of a substance from liquid to gaseous state at the boiling point. Heavy water: deuterium oxide used mainly in CANDU nuclear reactors. Heisenberg uncertainty principle: the more accurately one determines the position of a particle, the less accurately the momentum can be known, and vice versa. Hertz: unit of frequency equal to one event or cycle per second. Hole: absence of an electron in a semiconductor. Hookeï¿½s law: deformation of an object is proportional to force causing it.

Huygensï¿½ wavelets: model of spreading of waves in which each point on wavefront is source of circular or spherical waves. Hydraulic system: machines using fluids to transmit energy. Hyperbola: mathematical curve that describes an inverse relationship between two variables. Hypotenuse: side opposite the right angle in a triangle. -------------- Ideal mechanical advantage: in simple machine, the ratio of effort distance to resistance distance. Illuminance: rate at which electromagnetic wave energy falls on a surface. Illuminated object: object on which light falls. Image: reproduction of object formed with lenses or mirrors. Impulse: product of force and time interval over which it acts. Impulse-momentum theorem: impulse given to an object is equal to its change in momentum. Incandescent body: object that emits light because of its high temperature. Incident wave: wave that strikes a boundary where it is either reflected or refracted. Incoherent light: light consisting of waves that are not in step. Independent variable: variable that is manipulated or changed in an experiment. Index of refraction: ratio of the speed of light in vacuum to its speed in a material. Inelastic collision: collision in which some of the kinetic energy is changed into another form.

Inertia: tendency of object not to change its motion. Inertial mass: ratio of net force exerted on object to its acceleration. Initial velocity: velocity of object at time t=0. Instantaneous acceleration: acceleration at a specific time; slope of tangent to velocity- time graph. Instantaneous position: position of an object at specific time. Instantaneous velocity: slope of the tangent to position- time graph. Insulator: material through which the flow of electrical charge carriers or heat is greatly reduced. Interference fringes: pattern of dark and light bands from interference of light waves. Interference of waves: displacements of two or more waves, producing either large or smaller waves. Internal forces: forces between objects within a system. Intrinsic semiconductor: semiconductor in which conduction is by charges due to host material, not impurities. Inverse relationship: mathematical relationship between two variables, x and y, summarized by the equation xy=k, where k is a constant. Ionizing radiation: particles or waves that can remove electrons from atoms, molecules, or atoms in a solid. Isolated system: a collection of objects not acted upon by external forces into which energy neither enters nor leaves.

Isotope: atomic nuclei having same number of protons but different numbers of neutrons. -------------- The Letter J: Joule: SI unit of energy equal to one Newton-meter. Joule heating: increase in temperature of electrical conductor due to conversion of electrical to thermal energy. --------------- The Letter K: Kelvin temperature scale: scale with 0 K= absolute zero and 273.16 K = triple point of water. Keplerï¿½s laws: three laws of motion of bodies attracted together by the gravitational force. Kilogram: SI unit of mass. Kilowatt hour: amount of energy equal to 3.6 * 10^ 6 J. Usually used in electrical measurement. Kinematics: study of motion of objects without regard to the causes of this motion. Kinetic energy: energy of object due to its motion. Kinetic-molecular energy: description of matter as being made up of extremely small particles in constant motion. --------------- The Letter L: Laser: devise that produces coherent light by stimulated emission of radiation. Laser- induced fusion: proposed method of creating nuclear fusion by using heating caused by intense laser beams to squeeze matter together.

Law of conservation of energy: in a closed, isolated system, the total momentum is constant. Law of reflection: angle of incidence of a wave is equal to the angle of reflection. Law of universal gravitation: gravitational force between two objects depends directly on the product of their masses and inversely on the square of their separation. Lens: optical device designed to converge or diverge light. Lens equation: See mirror equation. Lenzï¿½s law: magnetic field generated by an induced current opposes the change in field that caused the current. Lepton: particle that interacts with other particles only by the electroweak and gravitational interactions. Lever arm: component of the displacement of the force from the axis of rotation in the axis of rotation in the direction perpendicular to the force. Light: electromagnetic radiation with wavelengths between 400 and 700 nm that is visible. Linear accelerator: device to accelerate subatomic particles by applying successive electric field. Linear relationship: relationship between two variables, x and y, summarized by the equation y= ax + b, where a and b are constant. Linear restoring force: force in direction toward equilibrium position that depends linearly on distance from distance from that position.

Liquid: materials that have fixed volume but whose shape depends on the container. Lodestone: naturally occurring magnetic rock. Longitudinal waves: wave in which direction of disturbance is the same as the direction of travel of wave. Loudness: physiological measure of amplitude of a sound wave; heard on pitch and tone color as well as amplitude. Lumen: unit of luminous flux. Luminance intensity: measure of light emitted by source in candelas; luminous flux divided by 4pie. Luminous flux: flow of light from source measured in lumens. Luminous object: object that emits light, as opposed to one that reflects light. Lux: unit of luminous flux; one lumen per square meter. ---------------- Machine: device that changes force needed to do work. Magnetic field: space around a magnet throughout which magnetic force exists. Magnification: ratio of size of an optical image to the size of the object. Manipulated variable: variable that the experimenter can change. Mass defect: mass equivalent of the binding energy; m=E/c^ 2 Mass number: number of nucleons ( protons plus neutrons) in the nucleus of an atom.

Mass spectrometer: device used to measure the mass of atoms or molecules. Matter wave: wave-like properties of particles such as electrons. Mechanical advantage: ratio of resistance force to effort force in a machine. Mechanical energy: sum of potential and kinetic energy. Mechanical resonance: condition at which natural oscillation frequency equals frequency of driving force; amplitude of oscillatory motion at a maximum. Mechanical wave: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave. Melting point: temperature at which substance changes from solid to liquid state. Meson: medium mass subatomic particle consisting of combination of a quark and antiquark. Meter: SI unit of length. Mirror equation: 1/do +1/di=1/f, where do is object distance, di is image distance, f is focal length. Moderator: material used to decrease speed of neutrons in nuclear reactor. Momentum: product of objectï¿½s mass and velocity. Monochromatic light: light of a single wavelength.

Mutual inductance: measures the amount of overlap between the magnetic flux produced in one coil and that which passes through a second coil, thus the amount of EMP induced in a secondary coil by the varying flux in the primary coil. Myopia: defect of eye, commonly called nearsightedness, in which distant objects focus in front of the retina. --------------- n-type semiconductor: semiconductor in which current is carried by electrons. Net force: vector sum of forces on object. Neutral: object that has no net electric charge. Neutrino: chargeless, massless, subatomic particle emitted with beta particles; type of lepton. Neutron: subatomic particle with no charge and mass slightly greater than that of proton; type of nucleon. Newton: SI unit of force. Newtonï¿½s law of motion: laws relating force and acceleration. Node: point where disturbances caused by two or more waves result in no displacement. Normal: perpendicular to plane of interest. Normal force: force perpendicular to surface. Nuclear equation: equation representing a nuclear reaction. Nuclear fission: reaction in which large nucleus splits into two parts, often approximately equal in mass. Nuclear fusion: reaction in which two nuclei are combined into one.

Nuclear reaction: reaction involving the strong force in which the number of protons or neutrons in a nucleus changes. Nuclear reactor: device in which nuclear fusion is used to generate electricity. Nuclear transmutation: change of one nucleus into another as the result of a nuclear reaction. Nucleon: either a proton or a neutron. Nuclide: nucleus of an isotope. --------------- Object: source of diverging light rays; either luminous or illuminated. Octave: interval between two frequencies with a ratio of two to one. Ohm: SI unit of resistance; one volt per ampere. Ohmï¿½s law: resistance of object is constant, independent of voltage across it. Opaque: material that does not transmit light. Open- pipe resonator: cylindrical tube with both ends closed and a sound source at one end. --------------- p-type semiconductor: semiconductor in which conduction is the result of motion of holes. Pair production: formation of particle and antiparticle from gamma rays. Parabolic mirror: mirror the shape of a paraboloid of revolution that has no spherical aberration. Parallel circuit: circuit in which there are two or more paths for current flow.

Parallel connection: connection of two or more electrical devices between two points to provide more than one current path. Pascal: SI unit of pressure; one neutron per square meter. Pascalï¿½s principle: pressure applied to a fluid is transmitted undiminished throughout it. Period: time needed to repeat one complete cycle of motion. Periodic motion: motion that repeats itself at regular intervals of time. Photoelectric effect: election of electrons from surface of metal exposed to electromagnetic radiation. Photon: quantum of electromagnetic waves; particle aspect of these waves. Photovoltaic cell: device that converts electromagnetic radiation into electrical energy. Physics: study of matter and energy and their relationship. Piezoelectricity: electric potential produced by deforming material. Pigment: colored material that absorbs certain colors and transmits or reflects others. Pitch: perceived sound characteristics equivalent to frequency. Planckï¿½s constant: ratio of energy of photon to its frequency. Plane mirror: flat, smooth surface that reflects light regularly. Plasma: state of matter in which atoms are separated into electrons and positive ions or bare nuclei. Point object: object idealized as so small to be located at only one position.

Polarized light: light in which electric fields are all in same plane. Position: separation between object and a reference point. Position- time graph: graph of objectï¿½s motion that shows how its position depends on clock reading, or time. Positron: antiparticle equivalent of electron. Potential difference: difference in electric potential between two points. Potential energy: energy of object due to its position or state. Potentiometer: electrical device with variable resistance; rheostat. Power: rate of doing work; rate of energy conversion. Precision: degree of exactness in a measurement. Pressure: force per unit area. Primary coil: transformer coil that, when connected to voltage source, creates varying magnetic flux. Primary light colors: red, green, or blue light. Primary pigment: yellow, green, or magenta light. Principal axis: line connecting center of curvature of spherical mirror with its geometric vertex. Line perpendicular to plane of lens passing through its center. Principle of superposition: displacement due to two or more forces is equal to vector sum of forces. Projectiles: motion of objects given initial velocity that then move only under force of gravity. Proton: subatomic particle with positive charge that is nucleus of hydrogen atom.

--------------- The Letter Q: quantized: a quantity that cannot be divided into smaller increments forever, for which there exists a minimum, quantum increment. Quantum mechanic: study of properties of matter using its wave properties. Quantum model of atom: atomic model in which only probability of locating electron is known. Quantum number: integer ratio of energy to its quantum increment. Quark: basic building block of protons, neutrons, other baryons, and mesons. Quark model: model in which all particles that interact via the strong interaction are composed of two or three quarks. --------------- Radiation: electromagnetic waves that carry energy. Radioactive decay: spontaneous change of unstable nuclei into other nuclei. Radioactive materials: materials that undergo radioactive decay. Range of projectile: horizontal distance between launch point of projectile and where it returns to launch height. Ray model of light: light may be represented by straight line along direction of motion. Ray optics: study of light using ray model. Rayleigh criterion: two optical images are separable if central bright spot of one image falls on first dark band of second. Real image: optical image at which rays from object converge. Receiver: device that detects electromagnetic waves.

Reference level: location at which potential energy is chosen to be zero. Reference point: zero location in a coordinate system or frame of reference. Refraction: change in direction of light ray when passing one medium to another. Refractive index: ratio of speed of light in vacuum to that in the medium. Resistance: ratio of potential difference across device to current through it. Resistance force: force exerted by a machine. Resistor: device designed to have a specific resistance. Responding variable: variable that changes as result of change in manipulated variable. Rest energy: energy due to mass of object; E= mc^ 2. Resultant: vector sum of two or more vectors. Right -hand rules: used to find force on current or moving particle in magnetic field; used to find direction of magnetic field caused by current or of induced EMF. Rutherfordï¿½s model of atom: nuclear model of atom; essentially all mass in compact, positively- charged object at center, surrounded by electrons. --------------- Scalar: quantity, like distance, that has only a magnitude, or size. Schematic diagram: representation of electric circuit using symbols.

Scientific notation: numbers expressed in form M * 10 ^ n , where 1< M < 10, and n is an integer. Scintillation: flash of light emitted when substance is struck by radiation. Second: SI unit of time. Second law of thermodynamics: heat flow only from region of high temperature o region of lower temperature. Secondary coil: transformer coil in which varying EMF is induced. Secondary light colors: yellow, cyan, or magenta light. Secondary pigment: red, green, or blue pigment. Self- inductance: induced EMF produced in coil by changing current. Semiconductor: material in which electrical conduction is smaller than that in a conductor, but more than in insulator. Series circuit: circuit in which electrical current flows through each component, one after another. Series connection: arrangement of electrical devices so that there is only one path through which current can flow. Short circuit: low resistance connection between two points, often accidental. SI: internationally agreed -upon method of using the metric system of measurement. Significant digit: reliable digits reported in a measurement. Simple harmonic motion: motion caused by linear restoring that has a period independent of amplitude of motion.

Simple machine: machine consisting of only one lever, inclined plane, wedge, screw, pulley, or wheel and axle. Sine: the ratio of the opposite side and the hypotenuse. Sliding friction: force between two surfaces in relative motion. Slope: ratio of the vertical separation, or rise to the horizontal separation, or run. Solid: state of matter with fixed volume and shape. Sound level: quantity measuring logarithm of sound intensity in decibels. Spark chamber: device used to detect path of charged subatomic particles by a spark that jumps along path of ionization created in a gas. Specific heat: thermal energy needs to change temperature of unit mass of substance one Kelvin. Spectroscope: device used to study spectrum of material. Spectrum: collection of wavelengths in electromagnetic spectrum. Speed: ratio of distance traveled to time interval. Speed of light: in vacuum, 2.9979458 * 10^8 m/s. Spherical aberration: inability of spherical mirror to focus all parallel rays to a single point. Standing wave: wave with stationary nodes. Static friction: force that opposes start of motion between two surfaces. Step- down transformer: transformer with output voltage smaller than input voltage.

Step- up transformer: transformer with output voltage larger than input voltage. Stimulated emission: emission of photon from excited atom caused by impact fo photon of same energy. Strong nuclear force: force of very short range that holds neutrons and protons in nucleus together. Superconductor: electrical conductor that has no resistance and low temperatures. Surface wave: wave on surface of liquid with characteristics of both longitudinal and transverse waves. Symmetry: property that is now charged when operation or reference frame is charged. Synchrotron: device to accelerate particles in which particles move in circular path. System: defined collection of objects. --------------- The Letter T: tangent: the ratio of the opposite side and the adjacent side. Temperature: measure of hotness of object on a quantitative scale. In gases, proportional to average kinetic energy of molecules. Terminal velocity: velocity of falling object reached when force of air resistance equals weight. Test charge: charge used, in principle, to measure electric field. Thermal energy: internal energy. Sum of kinetic and potential energy of random motion of particles making up object. Thermal equilibrium: state between two or more bodies where temperatures do not change. Thermal expansion: increase of length or volume of object due to change in temperature.

Thermometer: device used to measure temperature. Thermonuclear reaction: nuclear fusion. Thin- film interference: light interference caused by reflection from both front and rear surface of thin layer of liquid or solid. Timbre: sound quality or tone color; spectrum of sound frequencies that produce a complete wave. Time interval: difference in time between two clock readings. Tokamak: type of fusion reactor. Tone color: timbre or tone quality. Torque: product of force and the lever arm. Trajectory: the path followed by projectile. Transformer: device to transform energy from one electrical circuit to another by means of mutual inductance between two coils. Transistor: semiconductor device that controls large current by means of small voltage changes. Translucent: material transmitting light without but distorting its path. Transmutation: nuclear change from one element to another. Transparent: material transmitting light without distorting directions of waves. Transverse waves: wave in which disturbance is perpendicular to direction of travel of wave. Traveling wave: moving, periodic disturbance in a medium or field. Trigonometry: branch of math that deals with the relationship among angles and sides of triangles. Trough of wave: low point of wave motion, where displacement is most negative.

--------------- Uniform circular motion: motion in a circle of constant radius with constant speed. --------------- The Letter V: Valence band: in a solid, the range of energies of electrons that are bound to atoms. Vector quantity: quantity having both magnitude (size) and direction. Vector resolution: process of finding the effective value of a component in a given direction. Velocity: ratio of change in position to time interval over which change takes place. Velocity- time graph: plot of velocity of object as a function of time. Virtual image: point from which light rays appear to diverge without actually doing so. Viscous fluid: fluid that creates force that opposes motion of objects through it. The force is proportional to objectï¿½s speed. Volatile liquid: liquid that is easily vaporized. ---------------- Watt: unit of power, one joule per second. Wavelength: distance between corresponding points on two successive waves. Wave pulse: single disturbance moving through a medium or field. Weak boson: particle that carries or transmits the weak interaction of force. Weak interaction: force involved in beta decay of the neutron and atomic nuclei; one aspect of the electroweak force. Weight: force of gravity of an object.

Weightlessness: object in freefall, on which only the gravitational force acts. Wilson cloud chamber: chamber containing supersaturated vapor through which ionizing radiation leaves trails of visible droplets. Work: product of force and displacement in the direction of the force. Work function: energy needed to remove an electron from metal. Work energy theorem: work done on object is equal to the change in its kinetic energy. --------------- The Letter X: X ray: high- energy photons; high- frequency, short-wavelength electromagnetic waves. X-ray diffraction: A complicated technique using x-rays to "create an image" where no lense to focus the light rays is available. X-ray images: Images such as photographs or computer enhanced images produced by bombarding a target with x-rays. --------------- The Letter Y: Young's modulus: A constant of proportionality associated with the change in length of a material according to its elastic properties. --------------- Acceleration 1-D Kinematics - Lesson 1 - Describing Motion with Words Acceleration Speed and Velocity Acceleration The final mathematical quantity discussed in Lesson 1 is acceleration. An often confused quantity, acceleration has a meaning much different than the meaning associated with it by sports announcers and other individuals.

The definition of acceleration is: Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity . An object is accelerating if it is changing its velocity. Sports announcers will occasionally say that a person is accelerating if he/she is moving fast. Yet acceleration has nothing to do with going fast. A person can be moving very fast and still not be accelerating. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating. The data at the right are representative of a northward-moving accelerating object. The velocity is changing over the course of time. In fact, the velocity is changing by a constant amount - 10 m/s - in each second of time. Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration. The Meaning of Constant Acceleration Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned in the previous paragraph, the data table above show an object changing its velocity by 10 m/s in each consecutive second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second.

An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled! If an object is changing its velocity -whether by a constant amount or a varying amount - then it is an accelerating object. And an object with a constant velocity is not accelerating. The data tables below depict motions of objects with a constant acceleration and a changing acceleration. Note that each object has a changing velocity. Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value. A falling object for instance usually accelerates as it falls. If we were to observe the motion of a free-falling object ( free fall motion will be discussed in detail later), we would observe that the object averages a velocity of approximately 5 m/s in the first second, approximately 15 m/s in the second second, approximately 25 m/s in the third second, approximately 35 m/s in the fourth second, etc. Our free-falling object would be constantly accelerating.

Given these average velocity values during each consecutive 1-second time interval, we could say that the object would fall 5 meters in the first second, 15 meters in the second second (for a total distance of 20 meters), 25 meters in the third second (for a total distance of 45 meters), 35 meters in the fourth second (for a total distance of 80 meters after four seconds). These numbers are summarized in the table below. 0 s to End of Interval 0 – 1.0 s Note: The ~ symbol as used here means approximately. This discussion illustrates that a free-falling object that is accelerating at a constant rate will cover different distances in each consecutive second. Further analysis of the first and last columns of the data above reveal that there is a square relationship between the total distance traveled and the time of travel for an object starting from rest and moving with a constant acceleration. The total distance traveled is directly proportional to the square of the time. As such, if an object travels for twice the time, it will cover four times (2^2) the distance; the total distance traveled after two seconds is four times the total distance traveled after one second.

If an object travels for three times the time, then it will cover nine times (3^2) the distance; the distance traveled after three seconds is nine times the distance traveled after one second. Finally, if an object travels for four times the time, then it will cover 16 times (4^2) the distance; the distance traveled after four seconds is 16 times the distance traveled after one second. For objects with a constant acceleration, the distance of travel is directly proportional to the square of the time of travel. Calculating the Average Acceleration The average acceleration (a) of any object over a given interval of time (t) can be calculated using the equation This equation can be used to calculate the acceleration of the object whose motion is depicted by the velocity-time data table above. The velocity-time data in the table shows that the object has an acceleration of 10 m/s/s. The calculation is shown below. Acceleration values are expressed in units of velocity/time. Typical acceleration units include the following: m/s/s km/hr/s m/s2 These units may seem a little awkward to a beginning physics student. Yet they are very reasonable units when you begin to consider the definition and equation for acceleration.

The reason for the units becomes obvious upon examination of the acceleration equation. Since acceleration is a velocity change over a time, the units on acceleration are velocity units divided by time units - thus (m/s)/s or (mi/hr)/s. The (m/s)/s unit can be mathematically simplified to m/s2. The Direction of the Acceleration Vector Since acceleration is a vector quantity , it has a direction associated with it. The direction of the acceleration vector depends on two things: whether the object is speeding up or slowing down whether the object is moving in the + or - direction The general principle for determining the acceleation is: If an object is slowing down, then its acceleration is in the opposite direction of its motion. This general principle can be applied to determine whether the sign of the acceleration of an object is positive or negative, right or left, up or down, etc. Consider the two data tables below. In each case, the acceleration of the object is in the positive direction. In Example A, the object is moving in the positive direction (i.e., has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity.

Thus, this object has a positive acceleration. In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down. According to our general principle, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration. This same general principle can be applied to the motion of the objects represented in the two data tables below. In each case, the acceleration of the object is in the negative direction. In Example C, the object is moving in the positive direction (i.e., has a positive velocity) and is slowing down. According to our principle, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object has a negative acceleration. In Example D, the object is moving in the negative direction (i.e., has a negative velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object also has a negative acceleration. Observe the use of positive and negative as used in the discussion above (Examples A - D). In physics, the use of positive and negative always has a physical meaning.

It is more than a mere mathematical symbol. As used here to describe the velocity and the acceleration of a moving object, positive and negative describe a direction. Both velocity and acceleration are vector quantities and a full description of the quantity demands the use of a directional adjective. North, south, east, west, right, left, up and down are all directional adjectives. Physics often borrows from mathematics and uses the + and - symbols as directional adjectives. Consistent with the mathematical convention used on number lines and graphs, positive often means to the right or up and negative often means to the left or down. So to say that an object has a negative acceleration as in Examples C and D is to simply say that its acceleration is to the left or down (or in whatever direction has been defined as negative). Negative accelerations do not refer acceleration values that are less than 0. An acceleration of -2 m/s/s is an acceleration with a magnitude of 2 m/s/s that is directed in the negative direction. We Would Like to Suggest ... Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives.

We would like to suggest that you combine the reading of this page with the use of our Name That Motion Interactive. It is found in the Physics Interactive section and allows a learner to apply concepts of speed, velocity and acceleration.

Question: What is defined in physics as "the increase in velocity per unit of time"?
Answer: ACCELERATION